Whole+numbers+Theoretical+Background


 * __ Whole Numbers Theoretical Background __**

(Hot Maths Interactive Online, n.d.)

Big Ideas (Working Mother, n.d.)    // According to Van De Walle, Karp and Bay-Williams (2010) there are five big ideas that underpin place value. // **History of Place Value **
 * The major principle of base-ten numeration is the perception of sets of tens as single entities. Eg: Four sets of ten and 2 singles is a method for describing 42 single items/objects.
 * The major principle of place-value numeration involves the positioning of digits in numbers, that determine what they represent and which size group they count.
 * A symbolic pattern reflective of the 1-9 sequence is evident in each decade. These are the patterns to the way that numbers are formed.
 * Decomposition and composition of multi-digit numbers is a computation significant skill. Ones, tens and hundreds can be taken apart in different ways.
 * Real world life situations, are a way to understand "really big numbers". For example a 1000 or more may be difficult to conceptualize, however relating this to a meaningful concept such as a sports arena may be useful for those who have experienced such arenas.

** (Infolizer, n.d.) ** **Queensland Syllabus approach to Place Value** //The Mathematics Essential Learnings by year junctures guide educators when implementing lessons on place value.// "Whole Numbers (to 999) have position on a number line and each digit has a place value" (Queensland Studies Authority, 2007, p.2). "Whole Numbers (to 999) can be represented in different ways, including the use of concrete materials, pictorial materials, number lines and technologies" (Queensland Studies Authority, 2007, p.2) ** Key understandings of place value ** // According to Jamieson-Proctor (2010) there are 8 sequential step involved in the teaching of place value that educators should consider: //
 * Berlinghoff and Gouvea (2004) note the indian mathematicians as the inventers of the decimal numeration system.
 * The indian mathematicians introduced place value and created a dot, symbol or small circle to represent an empty place which resulted in the current numeration system (Berlinghoof & Gouvea, 2004).
 * According to Berlinghoof and Gouvea (2004), by the year 600 indian mathematicians were using place value systems based on powers of tens.
 * The Babylonians used a similar system to our current place value system, except it was a base 60 system instead of a base 10 system (Hodgkin, 2005).
 * Hodgkin ( 2005) outlines the Babylonian system, which includes the use of numbers from 1-59 without a zero sign.
 * Students are first introduced to whole numbers and place value during the early years by the end of the Year 3 juncture (Queensland Studies Authority, 2007).
 * The number organiser within the Essential Learnings syllabus addresses whole numbers and specific outcomes in regards to whole numbers.
 * Based on the previous group, gaining a picture of the next group by the use of PV charts, MAb's, pictures and patterns and real life contexts.
 * Learning to say the number name by emphasising place value rather than counting. Eg. A picture of three tens and one one. 3 tens and 1 one is 31.
 * Using a PV chart or numeral expander to introduce the symbols.
 * Reinforcing place value ideas
 * Using a numeral expander to learn how to regroup numbers, for example in the number 432 the number in the tens place is 3 but the number of tens in 432 altogether is 43.
 * Using materials and pictures to learn comparing strategies to establish the strategy and then using the strategy with symbols.
 * The sequencing of numbers
 * The adjustment of numbers (including rounding) to estimate or to mentally compute.

** Characteristics of the place value system ** (Math A Tube, n.d.)


 * According to Clausen-May (2005) place value determines the size and value of a number//.//
 * Place value determines the size in powers of ten, 1s, 10s, 100s, 1000s etc (Clausen-May, 2005).

Berlinghoff, W., & Gouvea, F. (2004). //Math through the Ages: A Gentle History for Teachers and Others.// America Oxton House Publishers Clausen-May, T. (2005). //Teaching Maths to Pupils with Different Learning Styles.// London: Sage publications Ltd. Hodgkin, L. (2005). //A history of mathematics from Mesopotamia to modernity.// Oxford: Oxford University Press. Hot Maths Interactive Maths Online. (n.d.). Whole Numbers [image]. Retrieved August 30, 2010 from [] Infolizer functional information system. (n.d.). //Babylonian number system// [image]. Retrieved September 10, 2010 from []

Jamieson-Proctor. (2010). EDX1280 Lecture 6 Week 6. Retrieved from http://usqstudydesk.usq.edu.au/file.php/15747/Week_6/Lecture_audio_Week_6.mp3

Math A Tube. (n.d.). //Place Values by four numbers// [image]. Retrieved September 10, 2010 from []

Queensland Studies Authority. (2007a). //Mathematics Essential Learnings by the end of Year 3.// Retrieved September 10, 2010 from []

Van De Walle, J., & Karp, K., & Bay-Williams, J. (2010). //Elementary & Middle School Mathematics Teaching Developmentally// (7th ed.). USA: Pearson Education.

Working mother. (n.d.). //Don't get burned by your lightbulb moment// **image**[|?]. Retrieved August 11, 2010 from []